Whilst your drive is admirable, the perception that you should BUY your own type rating in order to get employed is what is fundamentally wrong with this industry.
Take a look at an expat website like PPRuNe and read the whinging (whining) posts on differential pay, lower pay, CoS (Conditions of Service), time to upgrade and so on - realise that it's all a consequence of pilots giving up, by degrees, all that we and our predecessors worked for.
Yes, times are tough and work isn't that easy to get, and sacrifices have to be made...
Stand your ground. Don't do it. A type rating with no time on type isn't worth squat anyway. I wouldn't hire an ATR driver (irrespective of experience) with a B744/B777 "rating" and ZERO wide bodied time, international experience, ULH, ETOPS and all the other goodies that go with the B744/777 job package. You're a liability, not an asset, and there are many furlougees out there who will make your paper rating look absurd.
Save your money or buy Sirius stock. Double your money.
Your $20K for a B777 TR will be worth squat in 6 months.